This work presents a comparative theoretical analysis of spatial modal evolution in micro/nano-optical fiber (MNF) tapers. The study proposes the use of the Spectral Parameter Power Series (SPPS) Method and compares its performance with results from the so-called Exact Modes Method (EMM) and the Finite Element Method (FEM) (the method employed by the COMSOL© software in which the computations were implemented). By using these techniques, the modal analysis and intensity evolution are discussed along different sections of the optical fiber taper. Furthermore, the data are compared considering experimental values from a real micro/nano-optical fiber taper sample. The SPPS method offers a competitive accuracy and versatility to deal with graded index profiles, its computational costs are low, and its implementation is relatively easy. The results from the SPPS method fit to those of the EM method, which sometimes involves intricated models, and those of the FEM, which may require more computational time. The SPPS method offers an average relative error of less than 5% with respect to the exact method with less computational cost compared to the FEM method for radii bigger than 2 μm at 1550 nm.

A fractional-order model of a photovoltaic (PV) system is proposed in this paper. The system identification approach is used to develop an effective dynamical model for a PV system. A real PV module and a boost converter are used to gather the experimental input–output data for the identification process. The black box modeling is applied to the system identification to obtain the transfer function, without the requirement to perform any mathematical analysis. The identification process is based on the least squares criteria for minimizing model output error, and the Levenberg–Marquardt algorithm is used for optimizing the model parameters. The proposed fractional-order model (FOM) is investigated using MATLAB to study the frequency response and the model's stability. Simulation results verify the effectiveness and advantages of the FOM in comparison to identified integer-order model.